A Knapsack-Like Code Using Recurrence Sequence Representations

TL;DR

This paper introduces a novel cryptosystem based on unique integer representations via recurrence sequences, offering new disguising techniques and security arguments against common attacks.

Contribution

It develops a knapsack-like public key cryptosystem utilizing recurrence sequence representations with innovative disguising methods and security analysis.

Findings

Successfully constructs a cryptosystem based on recurrence sequences

Proposes new disguising methods for enhanced security

Provides security arguments against known attack vectors

Abstract

We had recently shown that every positive integer can be represented uniquely using a recurrence sequence, when certain restrictions on the digit strings are satisfied. We present the details of how such representations can be used to build a knapsack-like public key cryptosystem. We also present new disguising methods, and provide arguments for the security of the code against known methods of attack.